Answer
diverges to $-\infty$
Work Step by Step
This is a limit at infinity. Use Theorem 10.2.
(use only the highest powers)
$\displaystyle \lim_{x\rightarrow-\infty}f(x)=\lim_{x\rightarrow-\infty}\frac{2x^{4}}{1000x^{3}}$=...reduce...
$=\displaystyle \lim_{x\rightarrow-\infty}\frac{x}{500}$,
which is of determinate form $\displaystyle \pm\frac{\infty}{k}=\pm\infty$
(numerator negative, denominator positive)
So, the limit diverges to $-\infty$ .
